Each task is naturally associated with a certain length of MCMC trajectory. Image synthesis is most effective with shortrun trajectories (about 20 to 200 steps) that can rapidly generate new images. Adversarial defense requires midrun trajectories (about 1000 to 3000) that can preserve the class features while sampling removes adversarial signals. Density modeling requires longrun trajectories (50K steps or more) to ensure proper calibration of probability mass for the model steady-state. It is known that EBMs have a near universal tendency to learn a misaligned steady-state focusing on unrealistic images [1]}, and there are very few existing solutions to correct this. We intuitively refer to the spectrum of trajectories as the life cycle of an MCMC sample, from youth through middle age to maturity. Young samples have the highest quality visual appearance, middle age samples are useful for securing classifiers, and mature samples represent grounded knowledge of the data density (or lack thereof in the widespread case of a misaligned steady-state). Figure REF  illustrates the sampling paths that we study in this work.
